Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
398 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20261785 | C2 | semidirect |
| 2. #20261764 | C2 | semidirect |
| 3. D4×#11715897 | C2 | semidirect |
| 4. #20261756 | C2 | semidirect |
| 5. #20261754 | C2 | semidirect |
| 6. #20261739 | C2 | semidirect |
| 7. C2×C4⋊#11715897 | C2 | semidirect |
| 62. D4×C97 | M16 | semidirect |
| 108. C97 | #2990 | semidirect |
| 172. D4 | #13095521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261785 | 2 |
| #20261764 | 2 |
| D4×#11715897 | 2 |
| #20261756 | 2 |
| #20261754 | 2 |
| #20261739 | 2 |
| C2×C4⋊#11715897 | 2 |
| C4×#13095510 | 2 |
| #2990 | 97 |